# Orthogonal Self-Attention

arXiv: https://arxiv.org/abs/2602.05996 · HTML: https://mlsanity.com/paper/2602.05996/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm](https://mlsanity.com/paper/2505.16932/) (2025)
- [Rapid training of deep neural networks without skip connections or normalization layers using Deep Kernel Shaping](https://mlsanity.com/paper/2110.01765/) (2021)
- [Deep Transformers without Shortcuts: Modifying Self-attention for Faithful Signal Propagation](https://mlsanity.com/paper/2302.10322/) (2023)
- [Always Skip Attention](https://mlsanity.com/paper/2505.01996/) (2025)
- [Residual Connections Harm Generative Representation Learning](https://mlsanity.com/paper/2404.10947/) (2024)
- [Cutting the Skip: Training Residual-Free Transformers](https://mlsanity.com/paper/2510.00345/) (2025)

## Built on by (most cited first, 1 of 1)

- [NS-ATTENTION: Newton-Schulz Transformations of Attention Outputs in Vision Transformers](https://mlsanity.com/paper/2609.27735/) (2026)

## Abstract (arXiv)

Softmax Self-Attention (SSA) is a key component of Transformer architectures. However, when utilised within skipless architectures, which aim to improve representation learning, recent work has highlighted the inherent instability of SSA due to inducing rank collapse and poorly-conditioned Jacobians. In this work, we design a novel attention mechanism: Orthogonal Self-Attention (OSA), which aims to bypass these issues with SSA, in order to allow for (non-causal) Transformers without skip connections and normalisation layers to be more easily trained. In particular, OSA parametrises the attention matrix to be orthogonal via mapping a skew-symmetric matrix, formed from query-key values, through the matrix exponential. We show that this can be practically implemented, by exploiting the low-rank structure of our query-key values, resulting in the computational complexity and memory cost of OSA scaling linearly with sequence length. Furthermore, we derive an initialisation scheme for which we prove ensures that the Jacobian of OSA is well-conditioned.